Finding a desired point based on an objects velocity and rotation

Question

I'm looking to find the point that is 200 pixels in front of an enemy object. My method to try calculate this point is this:

//all sprites start facing down, so to begin with the point 200 pixels infront of the sprite is its current pos -200 on the y axis.
CGPoint predictedPoint = CGPointMake(self.position.x, self.position.y - 200);

//get the direction of this vector from the current position.
predictedPoint = [Utilities MinusVector:predictedPoint Vector2:self.position];
predictedPoint = [Utilities CGPointNormalize:predictedPoint];

//multiply it by 200 to get 200 pixels ahead.
predictedPoint = [Utilities MultiplyVector:predictedPoint Scalar:200];

//work out which way to rotate the enemy based on its velocity. (this code works as the enemies face the way they move!)
CGPoint facingVector = [Utilities MinusVector:self.position Vector2:CGPointMake(self.position.x + self.velocity.x, self.position.y + self.velocity.y)];
float theta = (atan2f(facingVector.y, facingVector.x) - SK_DEGREES_TO_RADIANS(90.0f));

//rotate
float cs = cosf(theta);
float sn = sinf(theta);

float px = predictedPoint.x * cs - predictedPoint.y * sn;
float py = predictedPoint.x * sn + predictedPoint.y * cs;

CGPoint thePoint = CGPointMake(px, py);

NSLog(@"Player x: %f. thePoint x: %f. Player y: %f. thePoint y: %f.", self.position.x, px, self.position.y, py);

Answer 1

So the calculation should be

green.center.x = triangle.center.x + 200 * cos( theta );
green.center.y = triangle.center.y + 200 * sin( theta );

where theta is the current rotation angle of the triangle. This assumes that theta == 0 has the triangle pointing to the right. If the 0 angle has the sprite pointing down, then I think you need to subtract M_PI_2, e.g.

green.center.x = triangle.center.x + 200 * cos( theta - M_PI_2 );
green.center.y = triangle.center.y + 200 * sin( theta - M_PI_2 );